Hi Eleonora,
I understand that you want to know the direction conventions followed by the UAV state vector.
The UAV Toolbox follows the North-East-Down Coordinate system with the z-coordinate of the UAV body frame, or 
pointing downwards when the UAV travels during perfect horizontal flight. Therefore, in the body frame, the Fthrust should indeed be negative and greater in magnitude than the weight of the UAV to gain altitude.
pointing downwards when the UAV travels during perfect horizontal flight. Therefore, in the body frame, the Fthrust should indeed be negative and greater in magnitude than the weight of the UAV to gain altitude. The UAV state indeed gives the coordinates in the inertial model as 
, 
, and 
. However, even in this frame, 
points downwards.
, , and . However, even in this frame, points downwards. The following code helps understand how the state output 
points downwards.
points downwards. model = multirotor;
s = state(model);
% Specify the location in world coordinates.
s(1:3) = [3;2;1];
u = control(model);
u.Roll = pi/12;
u.Thrust = 1;
e = environment(model);
sdot = derivative(model,s,u,e);
simOut = ode45(@(~,x)derivative(model,x,u,e), [0 3], s);
figure
plot(simOut.y(3,:));
legend('Z-position');
In the above code, with the specified thrust and roll angle, the multirotor should fly over and lose some altitude. However, the plot shows that the output z-position (
) is increasing. This is expected as positive 
is down as per the stated convention above.
) is increasing. This is expected as positive is down as per the stated convention above.The above code is taken from the example ‘Simulate A Multirotor Control Command’ in the documentation given below:
Please refer the sections ‘UAV Coordinate Systems’ and ‘UAV Multirotor Guidance Model Equations’ in the below documentation for more information.
Hope this helps.
